Finite Group Databasebeta

← #21445881

Subgroups — #21445881

Order 7808.

264 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519784C211yesmaximal, characteristic
2C2×#14519712C211yesmaximal, characteristic, complemented
3C2×#14519710C211yesmaximal, characteristic, complemented
4#16839763C211yesmaximal, characteristic
5#16839531C211yesmaximal, characteristic, complemented
6#16839530C211yesmaximal, characteristic, complemented
7C61×#417C211yesmaximal, characteristic
8#14519784—22no—
9#14519784C414yescomplemented
10C2×#11758194—21no—
11C2×#11758194C2211yescharacteristic
12C2×#11758194C2211yescharacteristic
13C22×#92418—21no—
14C22×#92418C2211yescharacteristic
15C2×C4⋊Dic61C2211yescharacteristic
16#14519712—22no—
17#14519710—21no—
18#14519710—21no—
19#14519701—21no—
20#14519698—21no—
21C2×#41×C61C2211yescharacteristic
22C2×M16×C61C2211yescharacteristic
23C2×C4⋊C4×C61C2211yescharacteristic
24#103×C61—21no—
25#102×C61—21no—
26#41×C61—21no—
27#41×C61—21no—
28#41×C61C2×C412yes—
29#41×C61Q812yes—
30C2×Q8×C61D411yescharacteristic
31C2×D4×C61—21no—
32C2×D4×C61D411yescharacteristic
33C22×C4×C61—21no—
34C22×C4×C61—21no—
35C22×C4×C61C2311yescharacteristic
36C22×Dic61—21no—
37M16×C61—21no—
38M16×C61—21no—
39C2×C8×C61—21no—
40C4⋊C4×C61—21no—
41C4⋊C4×C61—21no—
42C4⋊Dic61—21no—
43C4⋊Dic61—21no—
44#11758194—21no—
45#11758194—24no—
46#11758194—21no—
47#11758194—21no—
48#11758194C2×C412yes—
49C2×#92418—21no—
50C2×#92418—24no—
51C2×#92418—21no—
52C2×#92418C2×C412yes—
53C2×#92418D411yescharacteristic
54C2×#92418D411yescharacteristic
55C2×#92418D412yes—
56C23×C61—21no—
57C23×C61#4111yescharacteristic
58Q8×C61—21no—
59Q8×C61C4⋊C412yes—
60D4×C61—22no—
61D4×C61—22no—
62D4×C61—21no—
63D4×C61C4⋊C412yes—
64C2×C4×C61—21no—
65C2×C4×C61—22no—
66C2×C4×C61—22no—
67C2×C4×C61—41no—
68C2×C4×C61—81no—
69C2×C4×C61C22×C411yescharacteristic
70C2×C4×C61C2×D411yescharacteristic
71C2×C4×C61C2×D411yescharacteristic
72C2×C4×C61C2×D411yescharacteristic
73C2×C4×C61C2×Q811yescharacteristic
74C2×C4×C61#4111yescharacteristic
75C2×Dic61—41no—
76C2×Dic61—81no—
77C8×C61—41no—
78#92418—22no—
79#92418—41no—
80#92418C22⋊C412yes—
81#92418C22⋊C412yes—
82C22×C61—21no—
83C22×C61—21no—
84C22×C61—22no—
85C22×C61—41no—
86C22×C61—41no—
87C22×C61#11711yescharacteristic
88C22×C61#12111yescharacteristic
89C22×C61C22⋊Q811yescharacteristic
90C4×C61—22no—
91C4×C61—81no—
92C4×C61C2×C22⋊C411yescharacteristic
93C4×C61C2×C4⋊C411yescharacteristic
94C4×C61#12111yescharacteristic
95C4×C61C22⋊Q811yescharacteristic
96Dic61—81no—
97#1816—611nomaximal, Sylow
98C2×C61—21no—
99C2×C61—21no—
100C2×C61—42no—
101C2×C61#38011yescharacteristic
102C2×C61#47211yescharacteristic
103C2×C61#47311yescharacteristic
104C2×#131—611no—
105C2×#108—611no—
106C2×#107—611no—
107#417—611no—
108#417D6111yescharacteristic
109#343—611no—
110#343—611no—
111C61#181611yescharacteristic, complemented, Sylow
112C2×#41C2×D6111yescharacteristic
113#131—614no—
114#131—1222no—
115C2×M16—611no—
116C2×M16—611no—
117C2×M16—1221no—
118C2×M16C2×D6111yescharacteristic
119C22×C8—611no—
120C22×C8—1221no—
121C2×C4⋊C4—611no—
122C2×C4⋊C4C2×D6111yescharacteristic
123#108—1222no—
124#107—1221no—
125#107—1221no—
126#103—21no—
127#103—1221no—
128#102—21no—
129#102—1221no—
130#41—21no—
131#41—21no—
132#41Dic12212yes—
133#41C4×D6112yes—
134C2×Q8C22⋊D6111yescharacteristic
135C2×D4—21no—
136C2×D4C22⋊D6111yescharacteristic
137C22×C4—21no—
138C22×C4—21no—
139C22×C4—1221no—
140C22×C4C22×D6111yescharacteristic
141M16—21no—
142M16—21no—
143M16—612no—
144M16—1224no—
145M16—1221no—
146M16—1221no—
147M16—1221no—
148C2×C8—21no—
149C2×C8—612no—
150C2×C8—611no—
151C2×C8—611no—
152C2×C8—612no—
153C2×C8—1224no—
154C2×C8—1221no—
155C2×C8—1221no—
156C4⋊C4—21no—
157C4⋊C4—21no—
158C4⋊C4—1221no—
159C4⋊C4—1221no—
160C23—21no—
161C23#1175822411yescharacteristic
162Q8—21no—
163Q8#1175819612yes—
164D4—22no—
165D4—22no—
166D4—21no—
167D4#1175819612yes—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—41no—
172C2×C4—81no—
173C2×C4—4881no—
174C2×C4—2441no—
175C2×C4C2×Dic12211yescharacteristic
176C2×C4C2×C4×D6111yescharacteristic
177C2×C4D4×D6111yescharacteristic
178C2×C4D4×D6111yescharacteristic
179C2×C4#1175822411yescharacteristic
180C2×C4C2×C22⋊D6111yescharacteristic
181C8—41no—
182C8—612no—
183C8—612no—
184C8—1222no—
185C8—2441no—
186C22—21no—
187C22—21no—
188C22—22no—
189C22—41no—
190C22—41no—
191C22#1451973311yescharacteristic
192C22#1451974911yescharacteristic
193C22#1451975411yescharacteristic
194C4—22no—
195C4—81no—
196C4—4881no—
197C4C22⋊C4×D6111yescharacteristic
198C4C2×#1175819611yescharacteristic
199C4#1451974911yescharacteristic
200C4#1451975411yescharacteristic
201C2—21no—
202C2—21no—
203C2—42no—
204C2#1683962011yescharacteristic
205C2#1684003011yescharacteristic
206C2#1684003511yescharacteristic
subgroupG/H
centerC22#14519749
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#417C2
socleC22×C61#121
hypercenter#417D61
hypocenterC61#1816
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#14519712C2semidirect
3. C2×#14519710C2semidirect
5. #16839531C2semidirect
6. #16839530C2semidirect
9. #14519784C4semidirect
111. C61#1816semidirect